Finite Group Databasebeta

← #11754862

Subgroups — #11754862

Order 960.

472 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Dic15C211yesmaximal, characteristic, complemented
2C5×#936C211yesmaximal, characteristic, complemented
3C3×#4086C211yesmaximal, characteristic
4#91559C212yesmaximal, complemented
5#91548C212yesmaximal, complemented
6#91537C212yesmaximal, complemented
7#91534C212yesmaximal, complemented
8C4×#1204C211yesmaximal, characteristic, complemented
9Dic3×D20C211yesmaximal, characteristic, complemented
10#91368C211yesmaximal, characteristic, complemented
11Dic5×Dic6C211yesmaximal, characteristic, complemented
12#66015—31nomaximal, Hall
13C2×C3×C5×D4C2211yescharacteristic
14C22×Dic15C2212yes—
15C2×C5×Dic6C2211yescharacteristic
16C2×C3×C22⋊D5C2212yes—
17C2×C3×C22⋊D5C2212yes—
18C2×C3×D20C2211yescharacteristic
19C2×#1204C2211yescharacteristic
20C2×D5×Dic3C2212yes—
21#6719C2212yes—
22C4⋊Dic15C2211yescharacteristic
23C4×Dic15C2211yescharacteristic
24C5×#217C2212yes—
25C5×#217C2212yes—
26C4×C5×Dic3C2211yescharacteristic
27C3×C4×Dic5C2211yescharacteristic
28Dic3⋊Dic5C2211yescharacteristic
29Dic3⋊Dic5C2212yes—
30#6669C2211yescharacteristic
31#6668C2211yescharacteristic
32#6665C2212yes—
33#6665C2212yes—
34#6665C2212yes—
35Dic3×Dic5C2212yes—
36#5713—51nomaximal, Hall
37C5×#124—31no—
38#4093—31no—
39Q8×Dic5—31no—
40#4086D311yescharacteristic
41D4×Dic5—31no—
42#4032—32no—
43#4031—32no—
44#4029—32no—
45#4027—32no—
46C4×D20—31no—
47C4×Dic10—31no—
48C23×C3×C5C2312yes—
49C22×C3×D5C2312yes—
50C3×C5×D4—22no—
51C2×C3×C4×C5C2311yescharacteristic
52C2×Dic15—42no—
53C2×Dic15C2312yes—
54C2×Dic15C2311yescharacteristic
55C2×Dic15C2311yescharacteristic
56C2×C5×Dic3C2312yes—
57C2×C5×Dic3C2311yescharacteristic
58C2×C5×Dic3C2311yescharacteristic
59C5×Dic6—22no—
60C3×C22⋊D5—24no—
61C3×C22⋊D5—42no—
62C2×C3×Dic5C2311yescharacteristic
63C2×C3×Dic5C2311yescharacteristic
64C3×D20—22no—
65#1204—22no—
66D5×Dic3—42no—
67C3×#127—51no—
68#936—51no—
69#936—52no—
70#936D511yescharacteristic, complemented
71#935—52no—
72#935—52no—
73D4×Dic3—51no—
74D4×Dic3—52no—
75D4×Dic3—51no—
76C4×Dic6—51no—
77C4×Dic6—51no—
78C2×C5×Q8—31no—
79C2×C5×D4C2×D311yescharacteristic
80C2×C22⋊D5C2×D312yes—
81C2×C22⋊D5C2×D312yes—
82C22×Dic5—32no—
83C2×D20C2×D311yescharacteristic
84C2×C4×D5—32no—
85C2×Dic10—31no—
86C5×C22⋊C4—32no—
87C5×C22⋊C4—32no—
88C42×C5—31no—
89C22⋊Dic5—32no—
90#685—32no—
91#685—32no—
92#685—32no—
93C4⋊Dic5—31no—
94C4⋊Dic5—31no—
95C4⋊Dic5—32no—
96#683—31no—
97#683—31no—
98C4×Dic5—31no—
99C4×Dic5—32no—
100C4×Dic5C2×D311yescharacteristic
101#559—151noSylow
102C22×C3×C5—22no—
103C22×C3×C5—22no—
104C22×C3×C5—22no—
105C22×C3×C5C2411yescharacteristic
106C2×C3×D5—22no—
107C2×C3×D5—22no—
108C2×C3×D5—22no—
109C3×C4×C5#4112yes—
110Dic15—21no—
111Dic15—22no—
112Dic15—21no—
113C3×Dic5—21no—
114C3×Dic5#4112yes—
115C5×Dic3—21no—
116C5×Dic3—22no—
117C5×Dic3—21no—
118C2×C3×D4—52no—
119C2×C3×D4—52no—
120C2×C3×D4—51no—
121C2×C3×D4C2×D511yescharacteristic
122C22×Dic3—52no—
123C22×Dic3—52no—
124C2×Dic6—51no—
125C2×Dic6C2×D511yescharacteristic
126C3×C42—51no—
127#217—52no—
128#217—52no—
129#217—52no—
130#217—52no—
131#217C2×D512yes—
132#217C2×D512yes—
133C4⋊Dic3—51no—
134C4⋊Dic3—51no—
135Dic3⋊C4—51no—
136Dic3⋊C4—52no—
137Dic3⋊C4—51no—
138C4×Dic3—51no—
139C4×Dic3—52no—
140C4×Dic3C2×D511yescharacteristic
141C23×C5C22×D312yes—
142C22×D5C22×D312yes—
143C5×Q8—62no—
144C5×D4—22no—
145C2×C4×C5—32no—
146C2×C4×C5—31no—
147C2×C4×C5—31no—
148C2×C4×C5C22×D311yescharacteristic
149C22⋊D5—24no—
150C22⋊D5—42no—
151C2×Dic5—31no—
152C2×Dic5—31no—
153C2×Dic5—32no—
154C2×Dic5—122no—
155C2×Dic5C22×D311yescharacteristic
156C2×Dic5C22×D311yescharacteristic
157D20—22no—
158C4×D5—122no—
159Dic10—62no—
160#127—51no—
161#124—31no—
162#124—152no—
163#124—151no—
164#123—152no—
165#123—152no—
166C4×Q8—151no—
167C4×Q8—151no—
168C4×D4—151no—
169C4×D4—152no—
170C4×D4—151no—
171C2×C3×C5—42no—
172C2×C3×C5C2×#4111yescharacteristic
173C2×C3×C5C2×#4111yescharacteristic
174C2×C3×C5H(5,𝔽2)11yescharacteristic
175C3×D5—42no—
176C23×C3—52no—
177C23×C3C22×D512yes—
178C3×D4—22no—
179C3×D4—104no—
180C3×D4—102no—
181C3×D4—202no—
182C2×C3×C4—51no—
183C2×C3×C4—51no—
184C2×C3×C4C22×D511yescharacteristic
185C2×Dic3—52no—
186C2×Dic3—51no—
187C2×Dic3—51no—
188C2×Dic3—202no—
189C2×Dic3—202no—
190C2×Dic3C22×D512yes—
191C2×Dic3C22×D511yescharacteristic
192C2×Dic3C22×D511yescharacteristic
193Dic6—22no—
194Dic6—102no—
195C22×C5—22no—
196C22×C5—22no—
197C22×C5—22no—
198C22×C5C23×D311yescharacteristic
199C2×D5—22no—
200C2×D5—22no—
201C2×D5—22no—
202C4×C5—61no—
203C4×C5—62no—
204C4×C5—61no—
205C4×C5#23712yes—
206Dic5—21no—
207Dic5—61no—
208Dic5—62no—
209Dic5—61no—
210Dic5#23712yes—
211C2×Q8—31no—
212C2×Q8—151no—
213C2×D4—52no—
214C2×D4—52no—
215C2×D4—51no—
216C2×D4D3×D511yescharacteristic
217C22×C4—152no—
218C22×C4—152no—
219C4⋊C4—151no—
220C4⋊C4—151no—
221C4⋊C4—151no—
222C4⋊C4—152no—
223C4⋊C4—151no—
224C22⋊C4—32no—
225C22⋊C4—32no—
226C22⋊C4—152no—
227C22⋊C4—152no—
228C22⋊C4—152no—
229C22⋊C4—152no—
230C42—31no—
231C42—51no—
232C42—152no—
233C42—151no—
234C3×C5#55911yescharacteristic, complemented, Hall
235C22×C3—22no—
236C22×C3—22no—
237C22×C3—22no—
238C22×C3—102no—
239C22×C3—102no—
240C22×C3—102no—
241C22×C3C23×D511yescharacteristic
242C3×C4—52no—
243C3×C4—101no—
244C3×C4#71112yes—
245Dic3—22no—
246Dic3—21no—
247Dic3—21no—
248Dic3—101no—
249Dic3—102no—
250Dic3—101no—
251C2×C5—42no—
252C2×C5C2×#23711yescharacteristic
253C2×C5C2×#23711yescharacteristic
254C2×C5#100411yescharacteristic
255D5—42no—
256C23—52no—
257C23C2×D3×D512yes—
258Q8—62no—
259Q8—302no—
260D4—22no—
261D4—104no—
262D4—102no—
263D4—202no—
264C2×C4—31no—
265C2×C4—31no—
266C2×C4—32no—
267C2×C4—51no—
268C2×C4—51no—
269C2×C4—151no—
270C2×C4—152no—
271C2×C4—151no—
272C2×C4—602no—
273C2×C4—602no—
274C2×C4C2×D3×D511yescharacteristic
275C2×C3—42no—
276C2×C3—202no—
277C2×C3C2×#71111yescharacteristic
278C2×C3D5×#4111yescharacteristic
279C2×C3#414911yescharacteristic
280C5#571311yescharacteristic, complemented, Sylow
281C22—22no—
282C22—22no—
283C22—22no—
284C22—102no—
285C22—102no—
286C22—102no—
287C22C22×D3×D511yescharacteristic
288C4—52no—
289C4—61no—
290C4—61no—
291C4—62no—
292C4—101no—
293C4—301no—
294C4—302no—
295C4—301no—
296C4#678012yes—
297C3#6601511yescharacteristic, complemented, Sylow
298C2—42no—
299C2—202no—
300C2D5×#23711yescharacteristic
301C2#9202611yescharacteristic
302C2C2×#678011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×D4C22
prime radicalC3×#4086C2
hypercenterC2×D4D3×D5
hypocenterC3×C5#559
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. D4×Dic15C2semidirect
2. C5×#936C2semidirect
4. #91559C2semidirect
5. #91548C2semidirect
6. #91537C2semidirect
7. #91534C2semidirect
8. C4×#1204C2semidirect
9. Dic3×D20C2semidirect
10. #91368C2semidirect
11. Dic5×Dic6C2semidirect
70. #936D5semidirect
234. C3×C5#559semidirect
280. C5#5713semidirect
297. C3#66015semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D4×Dic152
C5×#9362
C3×#40862
#915592
#915482
#915372
#915342
C4×#12042
Dic3×D202
#913682
Dic5×Dic62
#660153
#57135